Problem 2: In this question you will solve the following initial value problem in three steps: (i) y" + y – 2y = 2t (ii) y(0) = 0, y'(0) =1 Step 1: Find the general solution of the associated homogeneous linear differential equation y" + y/ – 2y = 0 Step 2: Find one particular solution to the following inhomogeneous linear differential equation y" + y – 2y = 2t. (Hint: Use the method of undetermined coefficients to guess an appropriate trial solution yp(t).) Step 3: Use the answers you got in Steps 1 and 2 to find the solution to the original initial value problem: (i) y" + y' – 2y = 2t (ii) y(0) = 0, y'(0) = 1

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.